(a) Fit a linear regression model using all 20 observations. What are the values of a, b, r2, and se? (Round your answers to three decimal places.) a=b=r2=se=   (b) Fit a linear regression model with the two observations identified by arrows omitted. What are the values of a, b, r2, and se? (Round your answers to three decimal places.) a= b= r2= se=   (c) In a few sentences, describe any differences you found in parts (a) and (b). The y-intercept (increased/decreased/stayed the same) .The slope (increased/decreased/stayed the same) .The value of r2 (increased/decreased/stayed the same) .The value of se (increased/decreased/stayed the same).   (d) The researchers could use the estimated regression equation based on all 20 observations to make predictions for latitudes ranging from 58 to 64, or they could use the estimated regression equation based on the 18 observations (omitting the two observations identified by arrows) to make predictions for latitudes ranging from 58 to 61. Which strategy would you recommend, and why?   A) One would expect more accurate predictions from the line using 20 observations due to the decreased r2 value and increased se. B) One would expect more accurate predictions from the line using 18 observations due to the decreased r2 value and increased se.     C) The two lines would provide equally accurate predictions. D) One would expect more accurate predictions from the line using 20 observations due to the increased r2 value and decreased se. E) One would expect more accurate predictions from the line using 18 observations due to the increased r2 value and decreased se.

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15.3 #5

Models of climate change predict that global temperatures and precipitation will increase in the next 100 years, with the largest changes occurring during winter in northern latitudes. Researchers recently gathered data on the potential effects of climate change for flowering plants in Norway. The table below gives data for one flower species. A scatterplot of the "range of flowering dates" versus latitude for different sites in Norway is also shown. Two points that are potentially influential are indicated on the scatterplot.
A scatterplot has a horizontal axis labeled "Latitude" with values from 58 to 64 and a vertical axis labeled "Mean Flowering date range" with values from 10 to 50. The scatterplot has 20 points. A line goes down and right from (58.2, 32) to (63.4, 16.7). A pattern goes down and right becoming less steep from (58.2, 46) to (63.4, 11.8). The points are scattered moderately from the pattern. 0 points are on the line. The following 10 points are above the line. 
  • (58.7, 46) 
  • (58.2, 35.9) 
  • (58.2, 34.8) 
  • (59.4, 32.3) 
  • (60, 32.9) 
  • (59.4, 29.7) 
  • (60.8, 26.3) 
  • (60.9, 26.8) 
  • (63.4, 28.8) 
  • (63.4, 19.2)
 The following 10 points are below the line. 
  • (59.1, 27) 
  • (59.3, 26.2) 
  • (59.5, 25.7) 
  • (59.5, 27.6) 
  • (59.7, 19.2) 
  • (59.8, 24.4) 
  • (60.5, 22.4) 
  • (60.7, 17.9) 
  • (60.7, 13) 
  • (61.1, 11.8)
 The points (63.4, 28.8) and (63.4, 19.2) have arrows pointing towards them.

Flowering Range Versus Latitude: Anemone Hepatica

Latitude (N) Flowering
Date Range
58.7 46.0
58.2 35.9
58.2 34.8
59.4 32.3
60.0 32.9
59.4 29.7
59.1 27.0
59.3 26.2
59.5 25.7
59.5 27.6
59.7 19.2
59.8 24.4
60.8 26.3
60.9 26.8
63.4 28.8
63.4 19.2
60.5 22.4
60.7 17.9
60.7 13.0
61.1 11.8
(a)
Fit a linear regression model using all 20 observations. What are the values of abr2, and se? (Round your answers to three decimal places.)
a=b=r2=se=
 
(b)
Fit a linear regression model with the two observations identified by arrows omitted. What are the values of abr2, and se? (Round your answers to three decimal places.)
a=
b=
r2=
se=
 
(c)
In a few sentences, describe any differences you found in parts (a) and (b).
The y-intercept (increased/decreased/stayed the same) .The slope (increased/decreased/stayed the same) .The value of r2 (increased/decreased/stayed the same) .The value of se (increased/decreased/stayed the same).
 
(d)
The researchers could use the estimated regression equation based on all 20 observations to make predictions for latitudes ranging from 58 to 64, or they could use the estimated regression equation based on the 18 observations (omitting the two observations identified by arrows) to make predictions for latitudes ranging from 58 to 61. Which strategy would you recommend, and why?
 
A) One would expect more accurate predictions from the line using 20 observations due to the decreased r2 value and increased se.
B) One would expect more accurate predictions from the line using 18 observations due to the decreased r2 value and increased se.    
C) The two lines would provide equally accurate predictions.
D) One would expect more accurate predictions from the line using 20 observations due to the increased r2 value and decreased se.
E) One would expect more accurate predictions from the line using 18 observations due to the increased r2 value and decreased se.
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